The One-electron Quantum Hamiltonian in the Presence of EM Fields

The interaction between atoms or molecules and electromagnetic (EM) fields underlies all spectroscopic techniques and a great variety of desirable molecular properties. EM fields and EM waves are introduced via the famous Maxwell equations. The scalar and vector potential are defined, and the gauge freedom is outlined. The Coulomb gauge is adopted. The classical Hamiltonian for a charged particle in an EM field is derived, and from this the ‘minimal substitution’ rules for incorporating the fields in the quantum Hamiltonian are obtained. The operators describing the interaction of an electron with static electric and magnetic fields, including the magnetic fields from nuclear spins, are derived, followed by the derivation of the interaction between an electron and an EM wave.